For a project in her Geometry class, Sadie uses a mirror on the ground to measure the height of
her school’s football goalpost. She walks a distance of 6.45 meters from the goalpost, then
places a mirror flat on the ground, marked with an X at the center. She then walks 4.65 more
meters past the mirror, so that when she turns around and looks down at the mirror, she can
see the top of the goalpost clearly inarked in the X. Her partner measures the distance from her
eyes to the ground to be 1.55 meters. How tall is the goalpost? Round your answer to the
nearest hundredth of a meter.

Question

UpStudy AI · Accepted Answer

To determine the height of the goalpost using Sadie's mirror experiment, we can employ the concept of similar triangles.

### Step-by-Step Solution:

1. **Understand the Setup:**
   - **Distance from goalpost to mirror:** 6.45 meters
   - **Distance from mirror to Sadie:** 4.65 meters
   - **Height from Sadie's eyes to the ground:** 1.55 meters
   - **Height of the goalpost:** $$ h $$ meters (what we need to find)

2. **Use Similar Triangles:**
   - The triangles formed by the goalpost and Sadie are similar because the angle of incidence equals the angle of reflection.
   - This gives us the proportion:
     $$
     \frac{h}{6.45} = \frac{1.55}{4.65}
     $$

3. **Solve for $$ h $$:**
   $$
   h = 6.45 \times \left( \frac{1.55}{4.65} \right)
   $$
   $$
   h = 6.45 \times \frac{31}{93} = 6.45 \times \frac{1}{3} = 2.15 \text{ meters}
   $$

### Final Answer:
The height of the goalpost is **2.15 meters**.
The goalpost is 2.15 meters tall.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Geometry Questions